Mars has a mass of about 6.14 × 1023 kg,
and its moon Phobos has a mass of about
9.8 × 1015 kg.
If the magnitude of the gravitational force
between the two bodies is 4.18 × 1015 N,
how far apart are Mars and Phobos? The
value of the universal gravitational constant
is 6.673 × 10−11 N · m2/kg2.
The distance between Mars and Phobos can be calculated using the equation F = G*m1*m2/r^2, where F is the magnitude of the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of Mars and Phobos, respectively, and r is the distance between them. Rearranging the equation to solve for r, we get r = sqrt(G*m1*m2/F). Plugging in the given values, we get r = sqrt(6.673*10^-11*6.14*10^23*9.8*10^15/4.18*10^15) = 5.8*10^6 m. Therefore, the distance between Mars and Phobos is 5.8 million meters.
To find the distance between Mars and Phobos, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the universal gravitational constant (6.673 × 10^-11 N·m^2/kg^2)
m1 and m2 are the masses of the two bodies (Mars and Phobos)
r is the distance between the centers of the two bodies
In this case, we know the values for F, G, m1, and m2 and we need to solve for r.
Rearranging the formula, we have:
r^2 = (G * m1 * m2) / F
Taking the square root of both sides, we get:
r = sqrt((G * m1 * m2) / F)
Now we can plug in the given values:
r = sqrt((6.673 × 10^-11 N·m^2/kg^2) * (6.14 × 10^23 kg) * (9.8 × 10^15 kg) / (4.18 × 10^15 N))
Calculating this equation gives us:
r ≈ 8.11 × 10^6 meters
Therefore, Mars and Phobos are approximately 8.11 × 10^6 meters apart.
To find the distance between Mars and Phobos, we can use Newton's law of universal gravitation:
F = (G * M1 * M2) / d^2
Where:
F is the magnitude of the gravitational force
G is the universal gravitational constant
M1 and M2 are the masses of the two bodies
d is the distance between the centers of the two bodies
We can rearrange the formula to solve for the distance:
d = sqrt((G * M1 * M2) / F)
Now let's plug in the given values:
F = 4.18 × 10^15 N
G = 6.673 × 10^-11 N · m^2/kg^2
M1 = mass of Mars = 6.14 × 10^23 kg
M2 = mass of Phobos = 9.8 × 10^15 kg
Substituting these values into the equation:
d = sqrt((6.673 × 10^-11 N · m^2/kg^2 * 6.14 × 10^23 kg * 9.8 × 10^15 kg) / (4.18 × 10^15 N))
Now we can calculate the distance:
d = sqrt((4.091 * 10^29 N^2 · kg^2 · m^2) / (4.18 × 10^15 N))
d = sqrt(9.8065 * 10^13 m^2)
d = 9.9 × 10^6 m
Therefore, the distance between Mars and Phobos is approximately 9.9 million meters.